First, welcome to FT, PatekPhil -

I would definitely go with AA for the Plat Challenge, and moreover I would look at making the YVR-DXB runs on Cathay Pacific via HKG as often as via LHR. It's only an hour longer all in, and while the various lounges at LHR are fine, so are the CX lounges in YVR and HKG, plus going westbound rather than eastbound you might have less jetlag issues if that's a concern. Not to mention Cathay's business product is pretty nice...

In addition, if you'll be doing these laps of Ma Earth regularly, then a series of DONE3 RTWs, YVR-HKG-DXB-LHR-YVR, including staging for your flights to KBL (where do you fly from to get there - ISL?) might make a great deal of economic sense, especially compared to point-to-point J fares. If you bought the RTWs outside N. America (maybe in Asia on one of your trips) then you would also have quite a lot of N. America flying you could accomplish while you're in Canada between trips. Note you might run up against the minimum elapsed time rules on the RTWs (10 days?) if your trips are fast ones.

I would certainly crunch the numbers, but in any rate the sheer mileage accumulation you'd get with AA would seem to offer the best deal.